Some remarks on computing the square parts of integers

Abstract

Let n be a positive integer, and suppose n = Π p i a i is its prime factorization. Let θ(n) = Π p i a i − 1 , so that n θ (n) is the largest squarefree factor of n . We show that π is deterministic polynomial time Turing reducible to ϕ, the Euler function. We also show that θ is reducible to λ, the Carmichael function. We survey other recent work on computing the square part of an integer and give upper and lower bounds on the complexity of solving the problem.